Philosophy of Logic
Siavash Ahmadzadeh; Lotfollah Nabavi
Abstract
Naïve truth, T(x), is a predicate that applies to all of the sentences of the language and also for every sentence A of the language, T(˹A˺)↔A holds. Tarski for avoiding the liar paradox and trivializing of the language (theory) forced to withdraw from defining the naïve notion of truth ...
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Naïve truth, T(x), is a predicate that applies to all of the sentences of the language and also for every sentence A of the language, T(˹A˺)↔A holds. Tarski for avoiding the liar paradox and trivializing of the language (theory) forced to withdraw from defining the naïve notion of truth and he defined truth of every language in a metalanguage. Proponents of paraconsistency claim that by accepting paraconsistent logics we can retain the naïve truth predicate. A logic would be called paraconsistent if contradiction does not entail everything. But there is another paradox, the Curry paradox, which is related to conditionals and without using EFQ can trivialize naïve theories of truth. In this paper I will argue that although if we add arithmetic and naïve truth predicate to paraconsistent logics we would have a non-trivial theory, but for low deductive power, losing some prospected properties of naïve truth predicate and leaking of inconsistency to pure arithmetic parts, these logics will be unjustifiable.
Philosophy of Logic
Kourosh Arish
Abstract
The explanation of the meaning of logical connectives in this paper is under epistemological and semantic topics and has a philosophical-logical approach. Also, the field of philosophy of language and the relationship between grammar and logic is one of the other areas that have been addressed. After ...
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The explanation of the meaning of logical connectives in this paper is under epistemological and semantic topics and has a philosophical-logical approach. Also, the field of philosophy of language and the relationship between grammar and logic is one of the other areas that have been addressed. After establishing of classical logic, new logical systems appeared in the field with the aim of generalizing or modifying classical logic. The invalidity of some theorems of classical logic in these new reformed systems, which were called non-classical logic, created serious challenges and questions about the nature of logic. Quine is among those who, by proposing the theory of meaning-variance thesis, took a completely different position towards deviant logics. He judged between logics from an epistemological point of view and relying on natural language. His thesis was quite clear. "A change in logic is a change in the subject and actually a change in the meaning of logical connectives". Quine's thesis is generally accepted, but it also has critics. In the next step, the criticisms against Quine are described and evaluated. Meanwhile, the focus is on Putnam's criticism and his interpretation of the meaning of logical connectives. Also, Morten's criticisms from the perspective of the philosophy of language to Quine's thesis of meaning-variance have been described and evaluated. At the end, it is concluded that changing different logics does not always mean changing the subject and accepting the change of subject can not necessarily change the meaning of logical connectives.
Traditional Logic
Ali Reza Darabi
Abstract
In the tradition of Avicennian logic, there is a rule according to which there is a equivalence between two conditional hypothetical propositions that have the same quantity, different quality, the same antecedent, and the opposite consequent. This rule is called consequent negation. Avicennian logicians ...
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In the tradition of Avicennian logic, there is a rule according to which there is a equivalence between two conditional hypothetical propositions that have the same quantity, different quality, the same antecedent, and the opposite consequent. This rule is called consequent negation. Avicennian logicians disagree about this rule. Some of these logicians have proved this rule and some have rejected these proofs. In this article, we have tried to show the disagreements about these proofs are connected with the ambiguities in the tradition of Avicennian logic about the nature of singular conditional hypothetical propositions. Some of the evidences in Avicennian logic indicate that the appropriate connective for formulating the relationship between the antecedent and the consequent in connected Singular conditional hypotheticals are inflectional, and some evidences show this relationship as conditional. In this article, we have shown that this issue has had a serious impact on the existing disputes about the consequent negation rule
Standard Mathematical Logic
Fatemeh Shirmohammadzadeh Maleki
Abstract
In this article, first we define a Kripke semantics for normal modal Logic with a binary operator and we introduce a system K^2 which is sound and complete for this semantics. Then, we will introduce two translations and show that binary normal modal logic K^2, and unary normal modal logic K, i.e. modal ...
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In this article, first we define a Kripke semantics for normal modal Logic with a binary operator and we introduce a system K^2 which is sound and complete for this semantics. Then, we will introduce two translations and show that binary normal modal logic K^2, and unary normal modal logic K, i.e. modal logic with one binary operator, are very closely related by these two translations. We call a translation a faithful interpretation if provability is preserved in both directions. So, with this terminology we will show that these two translations are faithful interpretation of K into K^2 and vice versa. A logic extending K will be a set of formulas containing K closed under its rules and uniform substitution. A logic extending K^2 is similarly defined. Finally, we will prove that the classes of logics extending K and K^2 are closely related as well and there is a 1-1-correspondence between the logics extending K and extending K^2.
Non-Standard Mathematical Logic
Asadollah Fallahi
Abstract
Mortaza Hajhosseini in the second edition of his book Two Non-Classical Logic Systems, A new Outlook on Elements of Logic has introduced four non-classical logics: truth-functional, non-truth-functional, and combinations of the two, which are naturally extensions of the former two. In another article, ...
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Mortaza Hajhosseini in the second edition of his book Two Non-Classical Logic Systems, A new Outlook on Elements of Logic has introduced four non-classical logics: truth-functional, non-truth-functional, and combinations of the two, which are naturally extensions of the former two. In another article, we have examined Hajhosseini’s truth-functional logic, and in this article, we will discuss the non-truth-functional logic and its extension. In this article, we will only deal with formal-mathematical objections, and we will leave philosophical and non-formal objections as well as related historical materials to another article. In addition to some common flaws between Hajhosseini’s truth-functional and non-truth-functional logics, such as the vicious circle in the definition of the natural deduction system, the lack of an example for the condition of "normality of arguments" in semantics, incompleteness, and the inaccuracy of extra-problems, there are other flaws in the non-truth-functional logic. A formal problem is that many of the main rules in this system can be proven with the help of other main rules and thus are redundant. Another formal problem of the non-truth-functional logic is that it has a rule called " Hajhosseini’s rule" which causes every propositional variable in this system to be a theorem and the whole system becomes trivial. The third objection is that some forms of the distributivity rule in the expansion of the non-truth-functional logic of this book reduce the whole system to the classical logic of Frege and Russell.
Standard Mathematical Logic
Meghdad Ghari; Fatemeh Majlesi
Abstract
Justification Logic is a family of modal logics in which the proof or justification of a necessitated proposition can be explicitly expressed. These logics can be considered as epistemic logics in which the justification (reason or evidence) for knowledge or belief of a proposition can be expressed in ...
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Justification Logic is a family of modal logics in which the proof or justification of a necessitated proposition can be explicitly expressed. These logics can be considered as epistemic logics in which the justification (reason or evidence) for knowledge or belief of a proposition can be expressed in the language. In this paper, we study an extension of justification logics with actions. In particular, we extend the language of Artemov's logic of proofs with actions. To this end, we use the regular actions of propositional dynamic logic without the iteration operator. By combining the axiom system of the logic of proofs with that of propositional dynamic logic, we present an axiomatic proof system for this combined logic. We also present a possible world semantics, based on Kripke-Fitting models, for this combined logic, and prove the completeness theorem by means of the canonical model construction. We further establish the internalization property for this logic.
Analytical Philosophy
Saeed Masoumi
Abstract
Ramseyfication is one of the methods philosophers have proposed for formalizing structural realism. Ketland (2004), while providing explications about the Ramseyfication of theories and introducing some concepts related to it, presents a formulation of the Newman problem. He believes it can be almost ...
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Ramseyfication is one of the methods philosophers have proposed for formalizing structural realism. Ketland (2004), while providing explications about the Ramseyfication of theories and introducing some concepts related to it, presents a formulation of the Newman problem. He believes it can be almost said that the problem is as follows. The description of the theory, according to Ramsey’s way, in addition to empirical adequacy, only yields the cardinal number of entities in the world. In this article, in addition to providing a more precise formulation of Ketland about the Newman problem, we examine it. Furthermore, an explanation of the structural relationship between theory and the world will be presented based on definitions that are somehow given by borrowing from Ketland’s definitions, including “metaphysically correct structure” and “metaphysically and partially correct structure.” The structural consideration is also based on a definition of approximate truth, which is justified on the grounds of inference to the best explanation. We can give a plausible explanation of structural realism with the illustrations presented.
Traditional Logic
GHOLAMALI MOGHADDAM; alireza andarzgo
Abstract
AbstractWith regard to the division of carrying, into the primary essential predication and common technical predication , there have been differences of opinion in determining examples and matching with types, among others, there are opinions about the quality of predication the essentials together ...
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AbstractWith regard to the division of carrying, into the primary essential predication and common technical predication , there have been differences of opinion in determining examples and matching with types, among others, there are opinions about the quality of predication the essentials together and on the essence. It is well-known that carrying genus and differentia on species of each other is a common technical predication. Allameh Tabatabai considers the predication of genus and differentia to each other common technical predication and the predication of genus and differentia to species as the primary essential predication, as some like Allameh Javadi Amoli have introduced the predication of genus and differentia to each other and the predication of genus and differentia to type as the primary essential predication. It is possible that Allameh Tabatabai's point of view may be criticized and challenged, but it seems that according to the basis of Allameh's point of view, the criticisms raised can be answered. In this article, while analyzing the basis of Allameh in predication the essentials on the essence, some problems raised at the level of the theory have been investigated.Key words: Allameh Tabatabaei, primary essential predication common technical
Analytical Philosophy
Morteza Moniri
Abstract
First, in the light of Feferman’s views, we will examine Gödel’s dichotomy that either the capabilities of the human mind are beyond any finite machine, or there are Diophantine-type mathematical equations that are absolutely unsolvable. Then we examine Putnam’s argument that if ...
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First, in the light of Feferman’s views, we will examine Gödel’s dichotomy that either the capabilities of the human mind are beyond any finite machine, or there are Diophantine-type mathematical equations that are absolutely unsolvable. Then we examine Putnam’s argument that if scientific competence of the mind can be simulated by a Turing machine with the ability to prepare a list of scientific propositions, this machine will not print out the sentence that expresses this ability. In an effort to better understand this proof, we restate it in the language of modal logic. Then, we discuss the possibility of supertask computations to perform infinite basic operations in finite time. This is a possibility that has recently been proposed based on new physical theories. We argue that, assuming that such a possibility is realized, arithmetic will be determinate, meaning that the truth or falsity of each arithmetic sentence will be explainable.
Philosophical Logic
Fereshte Nabati
Abstract
Nowadays modal logic is one of the important areas of logic, but at the beginning of the emergence of modern logic, there was not much attention to this branch of logic, and even the founders of modern logic, including Russell, had an anti-modal position. One of the factors that led Russell to adopt ...
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Nowadays modal logic is one of the important areas of logic, but at the beginning of the emergence of modern logic, there was not much attention to this branch of logic, and even the founders of modern logic, including Russell, had an anti-modal position. One of the factors that led Russell to adopt such a position was the belief that logic is truth functional and extensional, and this is something that the introduction of modality destroys.Of course During the long period of his philosophical work, Russell has taken many and varied positions about modal notions. From the beginning, he did not have an anti-modal position. At first, he considered necessity as a description of an implication, and after some time, he introduced it as a primitive, basic and indefinable concept. Then, in some of his works, following Moore, he considered necessity as a kind of logical priority of propositions, but in the end he took an anti-modal position and tried to completely discard the modal notions. He said that these concepts are properties of propositional functions, not properties of propositions. But Russell has used second-order logic for explaining the modal concepts and explaining the difference between possibility and existence (which declares both of them to be properties of propositional functions), but even with this, he is not able to completely remove the modal notions from language and logic.
